Daily Practice · Higher
August 1998 - Higher 5-a-day
Every Higher sheet published in August 1998, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' August 1998 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1998Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 108 cm^3. Work out the volume of the smaller.
- 2nd August 199818 students study Spanish and 12 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 3rd August 1998A cumulative frequency graph is drawn for 116 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 4th August 1998Work out (18 x 10^9) / (9 x 10^3). Give your answer in standard form.
- 5th August 1998Work out the equation of the line parallel to y = 3x + 5 that passes through (6, 20).
- 6th August 1998A town's population is 17500 and grows by 8% each year. Work out the population after 5 years, to the nearest whole number.
- 7th August 1998A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 24 cm. Work out the other shorter side.
- 8th August 19984 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 9th August 1998A box plot has a minimum of 20 and a maximum of 37. Work out the range.
- 10th August 1998Write the recurring decimal 0.555... as a fraction in its simplest form.
- 11th August 1998A line has equation y = 5x + 2. Work out the gradient of any line perpendicular to it.
- 12th August 1998A block has volume 25 cm^3 and density 4 g/cm^3. Work out its mass.
- 13th August 1998ABCD is a cyclic quadrilateral. Angle ABC is 68°. Work out angle ADC.
- 14th August 199826 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 15th August 1998A box plot has minimum 15, lower quartile 18, median 20, upper quartile 27 and maximum 29. Work out the interquartile range.
- 16th August 1998Work out 216^(2/3).
- 17th August 1998For the curve y = 36/x, work out y when x = 4, and write down the equation of its vertical asymptote.
- 18th August 1998x : y = 3 : 4. Write y in terms of x.
- 19th August 1998A, B and C are points on a circle with centre O. Angle AOC is 56°. Work out angle ABC, where B is on the major arc.
- 20th August 19981 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 21st August 1998A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 22nd August 1998Write sqrt(50) in the form a sqrt(b), where b is as small as possible.
- 23rd August 1998Expand and simplify (x + 1)(x + 3)(x - 2).
- 24th August 1998A price rises by 25% and then falls by 25%. Work out the overall percentage change, to 2 decimal places.
- 25th August 1998A cone has base radius 10 cm and vertical height 24 cm. Work out its volume, leaving your answer in terms of pi.
- 26th August 199816 students study Spanish and 7 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 27th August 1998A histogram class is 5 units wide and contains 12.5 values. Work out the frequency density.
- 28th August 1998A meal deal has 9 mains, 6 sides and 3 drinks. How many different meals are possible?
- 29th August 1998Make x the subject of y = 9x^2 - 5.
- 30th August 1998y is inversely proportional to x. When x = 7, y = 15. Work out y when x = 5.
- 31st August 1998In triangle ABC, angle A is 69°, angle B is 61° and side a is 13 cm. Use the sine rule to work out side b, to 1 decimal place.